IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i9p857-d268040.html
   My bibliography  Save this article

Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

Author

Listed:
  • Helu Xiao

    (School of Business, Hunan Normal University, Changsha 410081, China)

  • Tiantian Ren

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Yanfei Bai

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Zhongbao Zhou

    (School of Business Administration, Hunan University, Changsha 410082, China)

Abstract

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model.

Suggested Citation

  • Helu Xiao & Tiantian Ren & Yanfei Bai & Zhongbao Zhou, 2019. "Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:857-:d:268040
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/9/857/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/9/857/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
    2. Jieming Zhou & Xiangqun Yang & Ya Huang, 2017. "Robust optimal investment and proportional reinsurance toward joint interests of the insurer and the reinsurer," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10733-10757, November.
    3. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    4. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    5. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    6. Wu, Huiling & Zeng, Yan, 2015. "Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 396-408.
    7. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    8. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    9. Waters, Howard R., 1983. "Some mathematical aspects of reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 17-26, January.
    10. O. L. V. Costa & R. B. Nabholz, 2007. "Multiperiod Mean-Variance Optimization with Intertemporal Restrictions," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 257-274, August.
    11. Duni Hu & Hailong Wang, 2018. "Time-consistent investment and reinsurance under relative performance concerns," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(7), pages 1693-1717, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zilan Liu & Yijun Wang & Ya Huang & Jieming Zhou, 2022. "Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yanfei Bai & Zhongbao Zhou & Rui Gao & Helu Xiao, 2020. "Nash Equilibrium Investment-Reinsurance Strategies for an Insurer and a Reinsurer with Intertemporal Restrictions and Common Interests," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
    2. Zhang, Hanwen & Dang, Duy-Minh, 2024. "A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 112-140.
    3. Zhang, Jingong & Tan, Ken Seng & Weng, Chengguo, 2017. "Optimal hedging with basis risk under mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 1-15.
    4. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    5. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    6. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    7. Li, Yongwu & Qiao, Han & Wang, Shouyang & Zhang, Ling, 2015. "Time-consistent investment strategy under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 187-197.
    8. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    9. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.
    10. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    11. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    12. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    13. Li, Yongwu & Li, Zhongfei, 2013. "Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 86-97.
    14. F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    15. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    16. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    17. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    18. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Oct 2024.
    19. Wu, Huiling & Chen, Hua, 2015. "Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching," Economic Modelling, Elsevier, vol. 46(C), pages 79-90.
    20. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:857-:d:268040. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.